evalIntCeil — Mathlib

Lean4
/-- Extension for the `positivity` tactic: `Int.ceil` is positive/nonnegative if its input is. -/
@[positivity ⌈_⌉]
def evalIntCeil : PositivityExt where
  eval {u α} _zα _pα
    e := do
    match u, α, e with
    | 0, ~q(ℤ), ~q(@Int.ceil $α' $ir $io $j $a) =>
      match ← core q(inferInstance) q(inferInstance) a with
      | .positive pa =>
        assertInstancesCommute
        pure (.positive q(int_ceil_pos (α := $α') $pa))
      | .nonnegative pa =>
        let _i ← synthInstanceQ q(IsStrictOrderedRing $α')
        assertInstancesCommute
        pure (.nonnegative q(Int.ceil_nonneg (α := $α') $pa))
      | _ =>
        pure .none
    | _, _, _ =>
      throwError"failed to match on Int.ceil application"
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